University:
Florida Gateway College
Course:
MAC 1140 | Precalculus
Academic year:

2019
Views:

493

Pages:

4
Author:

frankiebabyl3

Honors Pre-Calculus Derivatives Quiz Review Name:_________________________________ May 2013 Evaluate lim f ( x  h)  f ( x) to find the derivative. Show all work for full credit. Then evaluate h 0 h value for . 1. at the given 1.)_________________ ___________________ 2. 2.)_________________ ___________________ Use rules of differentiation to find . 3. 3.)_________________ 4. 4.)_________________ 5. 5.)_________________ 6. 6.)_________________ 7. 7.)_________________ 8. 8.)_________________ 9. 9.)_________________ 10. 10.)________________ Find the equation of the line tangent to the curve at the given value for . 11. 12. 13. 14. at 11.)________________ at 12.)________________ at 13.)________________ at 14.)________________ Use the first and second derivatives to identify the local max and min, inflection point (s) and determine the interval where the curve is concave up and/or concave down. Then graph the function (do not use a calculator). 15. 15. Local max__________________ Local min__________________ Pts of inflection_____________ Concave up (interval)________ Concave down (interval)______ 16. 16. Local max__________________ Local min__________________ Pts of inflection_____________ Concave up (interval)________ Concave down (interval)______ 17. 17. Local max__________________ Local min__________________ Pts of inflection_____________ Concave up (interval)________ Concave down (interval)______ 18. A rectangular plot of farmland will be bounded on one side by a river and on the other three sides by a singlestrand electric fence. With 800 m of wire at your disposal, what is the largest area you can enclose, and what are its dimensions? 18.)________________ ___________________ 19. A 216 m2 rectangular pea patch is to be enclosed by a fence and divided into two equal parts by another fence parallel to one of the sides. What dimensions for the outer rectangle will require the smallest total length of fence? How much fence will be needed? 19.)________________ ___________________ 20. Suppose represents revenue and represents cost, with units. Is there a production level that maximizes profit? If so, what is it? measured in thousands of 20.)________________ 21. A textile manufacturer has daily production costs of where is the total cost in dollars and is the number of units produced per day. How many units should be produced each day to yield a minimum cost? 21.)________________ 22. Find a number such that when its cube is subtracted from its square, the result is a maximum. 22.)________________ 23. A 12” x 12” square sheet of cardboard is to be used to make an open-top box by cutting a small square from each corner and bending up the sides. How large a square should be cut from each corner to make the box have as large a volume as possible? What is the maximum volume of the box? 23.)________________ 1. ; 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Local max: 16. Local max: 17. Local max: Local min: Local min: Local min: ; Pt. of Inf. Concavity up: ; Pt. of Inf. ; Pts. of Inf. ; Concave down: Concavity up: ; ; Concave down: ; Concavity up: 2 ; Concave down: 18. Largest area = 80,000m ; Dimensions: 200 m by 400 m 19. Dimensions: 12 m by 18 m; Total length required: 72 m 20. Yes, 1000 units 21. 122 units 22. 23. 2 inches; 128 in 3

Math Derivatives Review Answers

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